Q19 of 23 Page 771

Find the equation of the hyperbola with eccentricity and the distance between whose foci is 16.

Given: Eccentricity is , and the distance between foci is 16


Need to find: The equation of the hyperbola.


Let, the equation of the hyperbola be:


Distance between the foci is 16, i.e., 2ae = 16



And also given, the eccentricity, e =


Therefore,



---- (1)


We know that,


Therefore,


⇒


⇒ [Squaring both sides]


⇒


⇒ [From (1)]


So, the equation of the hyperbola is,


⇒ ⇒ [Answer]


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